SLAHQR(l) ) SLAHQR(l)NAME
SLAHQR - i an auxiliary routine called by SHSEQR to update the eigen‐
values and Schur decomposition already computed by SHSEQR, by dealing
with the Hessenberg submatrix in rows and columns ILO to IHI
SYNOPSIS
SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ,
IHIZ, Z, LDZ, INFO )
LOGICAL WANTT, WANTZ
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
PURPOSE
SLAHQR is an auxiliary routine called by SHSEQR to update the eigenval‐
ues and Schur decomposition already computed by SHSEQR, by dealing with
the Hessenberg submatrix in rows and columns ILO to IHI.
ARGUMENTS
WANTT (input) LOGICAL
= .TRUE. : the full Schur form T is required;
= .FALSE.: only eigenvalues are required.
WANTZ (input) LOGICAL
= .TRUE. : the matrix of Schur vectors Z is required;
= .FALSE.: Schur vectors are not required.
N (input) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER It is assumed that H is already upper
quasi-triangular in rows and columns IHI+1:N, and that
H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR works primarily with
the Hessenberg submatrix in rows and columns ILO to IHI, but
applies transformations to all of H if WANTT is .TRUE.. 1 <=
ILO <= max(1,IHI); IHI <= N.
H (input/output) REAL array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H. On exit, if WANTT is
.TRUE., H is upper quasi-triangular in rows and columns
ILO:IHI, with any 2-by-2 diagonal blocks in standard form. If
WANTT is .FALSE., the contents of H are unspecified on exit.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
WR (output) REAL array, dimension (N)
WI (output) REAL array, dimension (N) The real and imagi‐
nary parts, respectively, of the computed eigenvalues ILO to
IHI are stored in the corresponding elements of WR and WI. If
two eigenvalues are computed as a complex conjugate pair, they
are stored in consecutive elements of WR and WI, say the i-th
and (i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is
.TRUE., the eigenvalues are stored in the same order as on the
diagonal of the Schur form returned in H, with WR(i) = H(i,i),
and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
ILOZ (input) INTEGER
IHIZ (input) INTEGER Specify the rows of Z to which trans‐
formations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <=
ILO; IHI <= IHIZ <= N.
Z (input/output) REAL array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current matrix
Z of transformations accumulated by SHSEQR, and on exit Z has
been updated; transformations are applied only to the submatrix
Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not refer‐
enced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
> 0: SLAHQR failed to compute all the eigenvalues ILO to IHI in
a total of 30*(IHI-ILO+1) iterations; if INFO = i, elements
i+1:ihi of WR and WI contain those eigenvalues which have been
successfully computed.
FURTHER DETAILS
2-96 Based on modifications by
David Day, Sandia National Laboratory, USA
LAPACK version 3.0 15 June 2000 SLAHQR(l)